University of Wisconsin-Whitewater
Curriculum Proposal Form #3
New Course
Effective Term:
2151 (Spring 2015)
Subject Area - Course Number: MATH 450/650
Cross-listing:
(See Note #1 below)
Course Title: (Limited to 65 characters)
Graph Theory
25-Character Abbreviation:
Graph Theory
Sponsor(s):
Angela Harlan
Department(s):
Mathematical and Computer Sciences
College(s):
Letters and Sciences
Consultation took place:
NA
Programs Affected:
Yes (list departments and attach consultation sheet)
Departments:
Mathematics, Computer Science
Is paperwork complete for those programs? (Use "Form 2" for Catalog & Academic Report updates)
NA
Yes
Prerequisites:
with a B or better)
will be at future meeting
MATH 280, or CS 215 and (MATH 253 with a C or better, or MATH 250
Grade Basis:
Conventional Letter
S/NC or Pass/Fail
Course will be offered:
Part of Load
On Campus
Above Load
Off Campus - Location
College:
Letters and Sciences
Instructor:
Angela Harlan
Dept/Area(s): MATH
Note: If the course is dual-listed, instructor must be a member of Grad Faculty.
Check if the Course is to Meet Any of the Following:
Technological Literacy Requirement
Diversity
Writing Requirement
General Education Option: Select one:
Note: For the Gen Ed option, the proposal should address how this course relates to specific core courses, meets the goals of General Education in
providing breadth, and incorporates scholarship in the appropriate field relating to women and gender.
Credit/Contact Hours: (per semester)
Total lab hours:
Number of credits:
0
3
Total lecture hours:
Total contact hours:
48
48
Can course be taken more than once for credit? (Repeatability)
No
Yes
If "Yes", answer the following questions:
No of times in major:
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No of credits in major:
1 of 7
No of times in degree:
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No of credits in degree:
2 of 7
Proposal Information: (Procedures for form #3)
Course justification:
With the rapid growth of the Computer Science major, we are looking to the future of the program. Graph
theory is a topic that is utilized in many computer science fields. We would like to include a course on this
topic as an elective for the current major, as well as a requirement for the comprehensive major that is
under development. In addition, there is a plan to develop a master’s program in computer science, for
which a course in graph theory would be utilized.
Relationship to program assessment objectives:
This course will help students obtain the following mathematics SLO’s:
• Demonstrate mathematical thinking skills, progressing from a procedural and computational
understanding of mathematics to logical reasoning, pattern recognition, generalization, and
abstraction, and to a formal proof.
• Communicate mathematical ideas orally and in writing, with precision, clarity and organization, using
proper terminology and notation.
• Use knowledge of content and mathematical procedures to solve problems and make connections
between the different areas of mathematics.
This course will help students obtain the following computer science SLO:
• Each graduated student should have an understanding of the fundamental areas of Computer
Science discipline includes fundamentals of computing, programming languages, basic
foundation of mathematics, algorithms, computer architecture, design and implementation of
programs.
Budgetary impact:
In the beginning it is expected that the course will be taught once every two years. With the hiring of a
new faculty member specializing in mathematics education anticipated in Fall 2014, the two graph theory
experts in the math department will be able to cover the course as part of load.
Course description: (50 word limit)
This course will examine basic concepts and applications of graph theory. Topics covered will be selected
from trees, connectivity, paths and cycles, coloring, matching and covering problems, digraphs, and
network flows.
If dual listed, list graduate level requirements for the following:
1. Content (e.g., What are additional presentation/project requirements?)
Graduate students will be assigned additional readings and exercises, particularly more
theoretically based material. That is, there will be more proof writing from the graduate students.
2. Intensity (e.g., How are the processes and standards of evaluation different for graduates and
undergraduates? )
Graduate students will be held to a higher standard of mathematical communication. Their writing
will be expected to meet professional standards.
3. Self-Directed (e.g., How are research expectations differ for graduates and undergraduates?)
The additional material assigned to graduate students will be self-directed. Undergraduates will
not be expected to learn the material in a self-directed manner.
Course objectives and tentative course syllabus:
The course objectives are contained in the tentative course syllabus on the pages that follow.
Bibliography: (Key or essential references only. Normally the bibliography should be no more than one or two
pages in length.)
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Buckley, F., Lewinter, M., A Friendly Introduction to Graph Theory. Upper Saddle River: Prentice Hall,
2003. Print.
Chartrand, G. and Lesniak, L., Graphs and Digraphs. Boca Raton: CRC Press, 2005. Print.
Chartrand, G., and Zhang, P., A First Course in Graph Theory. Boston: Dover, 2012. Print.
Gould, R., Graph Theory. New York: Dover, 2012. Print.
Gross, J., Yellen, J., Graph Theory and its Applications, Second Edition. Boca Raton: CRC Press, 2006.
Print.
West, D., Introduction to Graph Theory, Second Edition. Upper Saddle River: Prentice Hall, 2001. Print.
The University of Wisconsin-Whitewater is dedicated to a safe, supportive and non-discriminatory learning
environment. It is the responsibility of all undergraduate and graduate students to familiarize themselves with
University policies regarding Special Accommodations, Academic Misconduct, Religious Beliefs Accommodation,
Discrimination and Absence for University Sponsored Events (for details please refer to the Schedule of Classes; the
“Rights and Responsibilities” section of the Undergraduate Catalog; the Academic Requirements and Policies and
the Facilities and Services sections of the Graduate Catalog; and the “Student Academic Disciplinary Procedures
(UWS Chapter 14); and the “Student Nonacademic Disciplinary Procedures" (UWS Chapter 17).
Course Objectives and tentative course syllabus with mandatory information (paste syllabus below):
Math – 450/650 Graph Theory
Spring 2015 – 01
Instructor:
Office:
Office Phone:
E-mail Address:
Office Hours:
MWF 9:55 – 10:45 in Hyer 216
Angela Harlan
2212 Laurentide Hall
472-5181
harrisak@uww.edu
W 1:30 – 3:30, TR 12:30 – 2:00 and by appointment
Prerequisites: Successful completion of Math 280, or successful completion of CS
215 and (MATH 253 with a C or better, or MATH 250 with a B or better).
Textbooks: A First Course in Graph Theory by Gary Chartrand and Ping Zhang,
Dover Publications, Inc., 2012.
Graph Theory by Ronald Gould, Dover Publications, Inc., 2012.
Course Description: This course will examine basic concepts and applications of
graph theory. Topics covered will be selected from trees, connectivity, paths and
cycles, coloring, matching and covering problems, digraphs, and network flows.
Course Objectives: Upon successful completion of this course the student will be able
to
 model mathematical problems using graph theory
 solve problems using various algorithms
 solve problems using graph-theoretical techniques
 write formal proofs using various techniques
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As a student you are expected to:

Attend all class sessions. If an extended absence is necessary, please inform
the instructor.

Work. It is expected that you will spend at least 6 – 9 hours per week on study
outside of class, which is the norm for any upper-level, three-credit class. As you
tackle individual problems, keep in mind the answer is just part of your work in this
course. It is the process you must understand and be able to explain. After all, that
is what will be expected of you in the future. Thus, discussions in class will focus on
conceptual understanding, and your work outside of class should do the same.
o Expectations for submitted work:

Any submission that is more than one sheet of paper must be stapled.

All problems must be in sequential order. You must use correct
mathematical “grammar.”

Succeed. If you are having problems understanding a topic, there is help
available. Come see me during my office hours or make an appointment with me
for a mutually agreeable time. It is best if you have tried the problems and come
with specific questions.

Be Aware of you Rights and Responsibilities as a Student (see the Student
Handbook). The University of Wisconsin-Whitewater is dedicated to a safe,
supportive and non-discriminatory learning environment. It is the responsibility of all
undergraduate and graduate students to familiarize themselves with University
policies regarding Special Accommodations, Academic Misconduct, Religious
Beliefs Accommodation, Discrimination and Absence for University Sponsored
Events (for details please refer to the Schedule of Classes: the “Rights and
Responsibilities” section of the Undergraduate Catalog; the Academic Requirements
and Policies and the Facilities and Services sections of the Graduate Catalog; and
the “Student Academic Disciplinary Procedures (UWS Chapter 14); and the
“Student Nonacademic Disciplinary Procedures” (UWS Chapter 17)).
Important Dates:
 February 2:
o Last day to change a grading basis
o Last day to drop with no “W” assigned
o Last day to drop for 100% refund
 February 27: Last day to drop a course
 February 27: No student shall be required to take more than two comprehensive
final examinations on the same day. Any student with more than two
comprehensive final examinations scheduled on the same day who wants to
reschedule the excessive examination(s) must make arrangements with the
instructors involved. If the student and instructors are unable to reach mutual
agreement about alternate arrangements, the student must notify the Registrar by
Friday, February 27. The Registrar shall arrange times as necessary with instructors
involved and shall notify the student of the arrangements by Monday, April 13.
Class conduct:

The use of cell phones is prohibited in the classroom at all times.
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
The use of laptops and tablets is prohibited in the classroom except for those
days on which I request you bring your laptop or tablet for classroom use.
Course work: In this course, you will have assignments, two in-class exams, and a
final exam. Each of these serves a purpose in your learning experience.
Assignments: There will be assignments each week, with the exception of exam
weeks. Problems will come from those found in the textbook, as well as from any
supplemental material I provide in class, and will be a combination of computations and
proofs. I have high expectations for your work, particularly when writing proofs. We will
discuss these expectations in class before the first assignment is due. Assignments
constitute 40% of your course grade. The purpose of these assignments is for you to
learn to use the various techniques taught in the course to solve problems. 
Exams: There will two in-class exams during the semester, which constitute 40% of
your course grade (20% each). The purpose of the exams is to assess your knowledge
of the course content.
Final Exam: The final exam is comprehensive/cumulative and constitutes 20% of your
course grade.
Make-up/Late Policy: I will allow make-up exams for an absence that I deem to be
excused. If you must miss an exam, you should contact me before the exam whenever
possible.
I do not accept late assignments. I will drop the lowest assignment grade.
Grades: Your final grade is composed of Activities (5%), Assignments (30%), two inclass Exams (20% each), and a comprehensive Final Exam (25%).
The grading scale that follows will be used, where x represents your grade. Note that
92.9 < 93 and is therefore an A- and not an A.
A:
A-:
B+:
B
B-:
C+:
C:
C-:
D+:
D:
D-:
F:
³ 93%
90% £ x < 93%
87% £ x < 90%
83% £ x < 87%
80% £ x < 83%
77% £ x < 80%
73% £ x < 77%
70% £ x < 73%
67% £ x < 70%
63% £ x < 67%
60% £ x < 63%
< 60%
Tentative Course Schedule*:
Week
1
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Topics Covered
Graphs and Models
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2
3
4
5
6
7
8
9
10
11
12
13
14
15
Connected Graphs
Common Classes of Graphs
Digraphs
Degree
Trees
Connectivity
Connectivity
Networks
Networks
Cycles and Circuits
Planarity
Matchings
Independence
Colorings
Ramsey Numbers
*Note: Instructors may choose to cover fewer topics in more detail, opting for depth of
knowledge rather than breadth of knowledge.
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